01:640:250 Lecture Notes - Lecture 7: If And Only If, Elementary Matrix
19 Feb 2016
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Properties of linear dependence & independence: the set containing only is linearly dependent. In fact, any set containing { 0} is linearly dependent. { 0, u1 , u2, , uk } V 0 , then the set t ={ v } is linearly independent. If you have a set containing more than n vectors in rn dependent: there aren"t enough columns to have enough pivots are scalar multiples of each other, the v is linearly dependent. If you have a set of vectors s={ u1 , u2 , , uk } , and removing any vector changes span(s ) Recall a x= b is a matrix representation of a linear system of m equations with n variables. If a x= 0 this is a matrix representation of a homogeneous linear system: This system will never be inconsistent since the last column is 0 and inconsistent matrices have a nonzero value in the last column.
